HP 40gs HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 310

Analyzing vector motion and collisions Ship A is currently at position vector 21i + 21j km and is currently traveling at a velocity of -4i + 6j km/hr. Ship B is at 30j and traveling at 2i + 3j km/hr. If the ships continue on their present courses, show that they will not collide and find the distance between them at the time of their closest approach. The advantage of the approach shown here is that it is very visual. Obviously there are other methods based purely on calculations. Firstly enter the equations for the ships' paths into the Parametric aplet using the first equation pair for ship A and the second for ship B. Making a guess at the ships' behavior and position, I will set up the axes as shown on the right. I am assuming that the collision will occur in the first 6 seconds and in the axes range chosen. This can always be adjusted if my guess is wrong. The reason for choosing -15 on the YRng is to ensure that the x axis is visible on the screen. Notice in the second screen that Simult: must be checked if the plot is to be a good illustration of the ship's movements. If you've done this correctly then you will see the ship's movements on the plot view. Careful examination of the paths of the ships as they appear on the screen will show visibly that they do not collide. The graph is shown on the right just before closest approach. However we need to verify this. The formula for the distance between the ships is d = ( x1 − x2 )2 + ( y1 − y2 )2 and this can now be entered into the Function aplet as shown right. With an equation this complex it is probably worth checking with the key that you have typed it correctly. Notice that the active variable in Function must be X not the T used in Parametric. 310